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Math 210: Calculus I

This is a collection of video lectures for Math 210: Calculus I from UMKC (University of Missouri-Kansas city). Consisting of 31 lectures taught by Professor Richard Delaware, this course introduces the concepts and techniques of differential calculus and integral calculus. The topics covered here include a review of precalculus, limits of functions, the derivative of a function, applications of differential calculus, the integral of a function, and applications of integral calculus.

Unit 2 - The Derivative of a Function

Lecture 10 - What is a Derivative?
Definition of the Derived Function: The "Derivative", & Slopes of Tangent Lines. Instantaneous Velocity. Functions Differentiable (or not!) at a Single Point. Functions Differentiable on an Interval.

Lecture 25 - Area Defined as a Limit
The Sigma Shorthand for Sums. Summation Properties & Handy Formulas. Definition of Area "Under a Curve". Net "Area". Approximating Area Numerically.

Lecture 26 - The Definite Integral
The Definite Integral Defined. The Definite Integral of a Continuous Function = Net "Area" Under a Curve. Finding Definite Integrals. A Note on the Definite Integral of a Discontinuous Function.

Lecture 31 - Average Value of a Function, Work
Average (Mean) Value of a Continuous Function. Work Done by a Constant Force. Work Done by a Variable Force. Do-It-Yourself Integrals: Pumping Fluids. Work as Change in Kinetic Energy.